How do you find the sin of theta if sin of theta is radical 5 times cos of theta and 0<theta<pi/2?

Question

How do you find the #sinθ# if #sinθ=sqrt(5cosθ)# and 0<θ<#pi/2#?

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Answer 1 · 2018-05-06T03:36:47

No solution.

#"Given : " sin theta = sqrt(5 cos theta), theta in 0 < pi/2#

#sin^2 theta = 5 cos theta, color(crimson)(" squaring both sides"#

#1 - cos^2 theta = 5 cos theta, color(crimson)(" as " sin^2 theta + cos^2 theta = 1#

#cos^2 theta + 5cos theta - 1 = 0#

#Let cos theta = x#

#x^2 + 5 x - 1 = 0#

#x = (-5 +- sqrt(5^2 -4 * 1 * 1 )) / (2*1)#

#x = (-5 +-sqrt21) / 2#

#x =(-5 +- 4.9) /2#

#x = -0.05, -4.95#

#cos theta = -0.05, cancel(-4.05), " as cos can have a value between -1 and 1"#

#cos theta = -0.05#

#"Since " theta in 0 < pi/2, " where cos is always positive, we cannot have a solution for the given sum."#